- Packing circles in a square: new putative optima obtained via global optimization Bernardetta Addis (b.addising.unifi.it) Marco Locatelli (locatelldi.unito.it) Fabio Schoen (schoening.unifi.it) Abstract: The problem of finding the optimal placement of $N$ identical, non overlapping, circles with maximum radius in the unit square is a well known challenge both in classical geometry and in optimization. A database of putative optima is currently maintained at \url{www.packomania.com}. Recently, through clever use of an extremely simple global optimization method, we succeeded in finding improved configurations for several instances. The improved configurations are in the range $N \leq 90$, i.e., they improve even over relatively small instances (even $N=53$), an event that some researchers did not believe to be possible. We also improved larger instances using a simpler strategy initialized at the previously known putative optimum. Keywords: circle packing, basin hopping, global optimization Category 1: Global Optimization Category 2: Global Optimization (Stochastic Approaches ) Category 3: Global Optimization (Applications ) Citation: DSI report 01/2005 Dipartimento di Sistemi e Informatica Universita' di Firenze Download: [PDF]Entry Submitted: 03/04/2005Entry Accepted: 03/04/2005Entry Last Modified: 03/07/2005Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.